1003C - Intense Heat

C. Intense Heat

time limit per test

4 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

The heat during the last few days has been really intense. Scientists from all over the Berland study how the temperatures and weather change, and they claim that this summer is abnormally hot. But any scientific claim sounds a lot more reasonable if there are some numbers involved, so they have decided to actually calculate some value which would represent how high the temperatures are.

Mathematicians of Berland State University came up with a special heat intensity value. This value is calculated as follows:

Suppose we want to analyze the segment of $n$ consecutive days. We have measured the temperatures during these $n$ days; the temperature during $i$-th day equals $a_i$.

We denote the average temperature of a segment of some consecutive days as the arithmetic mean of the temperature measures during this segment of days. So, if we want to analyze theaverage temperature from day $x$ to day $y$, we calculate it as $\frac{\sum _{i=x}^y{a}_i}{y-x+1}$ (note that division is performed without any rounding). The heat intensity value is the maximum of average temperatures over all segments of not less than $k$ consecutive days. For example, if analyzing the measures $[3,4,1,2]$ and $k=3$, we are interested in segments $[3,4,1]$, $[4,1,2]$ and $[3,4,1,2]$ (we want to find the maximum value of average temperature over these segments).

You have been hired by Berland State University to write a program that would compute the heat intensity value of a given period of days. Are you up to this task?

Input

The first line contains two integers $n$ and $k$ ($1\le k\le n\le 5000$) — the number of days in the given period, and the minimum number of days in a segment we consider when calculating heat intensity value, respectively.

The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($1\le a_i\le 5000$) — the temperature measures during given $n$ days.

Output

Print one real number — the heat intensity value, i. e., the maximum of average temperaturesover all segments of not less than $k$ consecutive days.

Your answer will be considered correct if the following condition holds: $|res-re{s}_0|<{10}^{-6}$, where $res$ is your answer, and $re{s}_0$ is the answer given by the jury's solution.

Example

input

Copy

4 3
3 4 1 2

output

Copy

2.666666666666667

题意：计算一段时内，不少于连续k天最高的平均温度。The heat intensity value is the maximum of average temperatures over all segments of not less than $k$ consecutive days

题解：暴力  这道题坑点可能读题，没读好，昨晚一直wa8，这会看下，有精度误差，再看别人代码，不一定是除k，在仔细看题，发现是至少是k天，一直以为是计算k天温度的最大值。

c++：

include<bits/stdc++.h>
using namespace std;
double n,k,a[5010],sum,ans;
int main()
{
    cin>>n>>k;
    for(int i=1; i<=n; i++)
        cin>>a[i],a[i]+=a[i-1];
    for(int i=k; i<=n; i++)
    for(int j=i;j<=n;j++)
        ans=max(ans,(a[j]-a[j-i])*1.0/i);
    cout<<fixed<<ans<<endl;
    return 0;
}